Comparing – Adding – Subtracting Mixed Numbers

To compare, add or subtract mixed numbers, first convert each mixed number to an improper fraction.

Then follow the same procedure you learned for comparing, adding and subtracting fractions:

Convert each fraction to its equivalent fraction so that all the fractions have the same denominator (the least common denominator).

Then:

To add the fractions – add up all the numerators.

To subtract the fractions – subtract one numerator from the other numerator.

add 4 2/3 + 7 3/5 =

• First, convert the mixed numbers to improper fractions:

4 2/3 = 14/3

7 3/5 = 38/5

14/3 + 38/5 = ?

• Now find the least common denominator.
• The common denominators for 14/3 are: 3,6,9,15,18…
• The common denominators for 38/5 are: 5,10,15,20,25,…
• The least common denominator for 14/3 and 38/5 is: 15
• The equivalent fraction for 14/3 with a denominator of 15 is: 70/15

(multiply the numerator and the denominator by 5)

• The equivalent fraction for 38/5 with a denominator of 15 is: 114/15

(multiply the numerator and denominator by 3)

70/15 + 114/15 = 184/15

And we could subtract these mixed numbers:

(4 2/3 – 7 3/5) = (70/15 - 114/15) = - 44/15.

Notice: when we add or subtract the fractions, the common denominator stays the same, and we add or subtract the numerators.